Uber has threatened to fire an engineer accused by Alphabet's self-driving Waymo unit of stealing confidential documents in a high-profile trade secrets case between the two companies, according to a court filing.

The case, which pits two companies battling to dominate the fast-growing field of self-driving cars, hinges on Waymo allegations that the information Levandowski took made its way into Uber's Lidar system, a key sensor technology in self-driving cars.

U.S. District Judge William Alsup in San Francisco last week issued an injunction ordering Uber to keep Levandowski away from work involving the self-driving car technology at issue in the case, to prevent him and all other employees from using the materials and to return them to Waymo by May 31.

Uber has told Levandowski that he must comply with the order to return Waymo documents or face possible termination, Levandowski's lawyers said in a court filing on Thursday.

The lawyers asked the judge to modify his order so that Uber is not required to fire Levandowski if the engineer asserts his constitutional rights against self-incrimination and refuses to produce documents.

Uber representatives could not immediately be reached for comment on Levandowski's filing, and a Waymo spokesman declined to comment.

Earlier on Thursday Uber said it would appeal a judge's order rejecting its attempt to arbitrate Waymo's trade secret claims, according to a court filing. Alsup last week ruled that Waymo's lawsuit should not be heard in a private forum, and instead should continue to be litigated on San Francisco federal court.

Levandowski left Waymo in January 2016 and started Otto, a self-driving truck startup that Uber bought for $680 million in August. He had until last month run Uber's self-driving car division, before stepping aside from those responsibilities pending the court case.

Uber has not denied that Levandowski took Waymo documents, but says it has not used any Waymo technology in its cars. In his injunction order, Alsup said "few" of Waymo's alleged trade secrets have been traced to Uber's self-driving car technology, and that Waymo's patent claims against Uber have proved meritless.